A person bending forward to lift a load \"with his back\" (Fig. P10.71a) rather

Question

A person bending forward to lift a load "with his back" (Fig. P10.71a) rather than "with his knees" can be injured by large forces exerted on the muscles and vertebrae. The spine pivots mainly at the fifth lumbar vertebra, with the principal supporting force provided by the erector spinalis muscle in the back. To see the magnitude of the forces involved and to understand why back problems are common among humans, consider the model shown in Fig. P10.71b for a person bending forward to lift a W = 214 N object. The spine and the upper body are represented as a uniform horizontal rod of weight 350 N, pivoted at the base of the spine. The erector spinalis muscle, attached at a point two thirds of the way up the spine, maintains the position of the back. The angle between the spine and this muscle is = 13.1°. Find the tension in the back muscle and the compressional force in the spine. tension N compressional force N

Explanation / Answer

Take the length of the spine as 1 unit.

You have a horizontal bar with the forces

Rx and Ry at x = 0 (reactions at the hips)
350N down at x = 0.5 (weight of spine)
T at angle 13.1 degrees, at x = 0.6667 (muscle)
214 N down at x = 1 (weight being lifted).

Take moments about x = 0.
0.5 x 350 + 1 x 214 = 0.6667 x T sin 13.1
T = 2574.31 N = 2.57 kN

Resolve horizontally

Rx = T cos 13.1 = 2507.32 N = 2.51 kN

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